Question

3.) polygon p is dilated to get polygon q.
a.) what is the value of y? show work.
b.) what is the scale factor?

Explanation:

Step1: <Determine the scale factor>

Since the polygons are similar (due to dilation), the ratio of corresponding sides gives the scale factor. For the sides \(3\) and \(4\) (from polygon \(Q\) to \(P\)), the scale factor \(k\) from \(Q\) to \(P\) is \(\frac{4}{3}\). But if we consider from \(P\) to \(Q\) (since \(P\) is dilated to \(Q\)), the scale factor \(k=\frac{3}{4}\). Also, using another pair of sides: \(\frac{y}{6}=\frac{3}{4}\) (because of the proportion of corresponding sides in similar polygons \(y\) (side of \(Q\)) and \(6\) (side of \(P\))).

Step2: <Solve for \(y\)>

From \(\frac{y}{6}=\frac{3}{4}\), cross - multiply. We get \(4y = 3\times6\). Then \(4y=18\), and \(y=\frac{18}{4}=\frac{9}{2}=4.5\).

Answer:

a. \(y = 4.5\)
b. The scale factor is \(\frac{3}{4}\)